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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Functions with a closed graph


Author: Ivan Baggs
Journal: Proc. Amer. Math. Soc. 43 (1974), 439-442
MSC: Primary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1974-0334132-8
MathSciNet review: 0334132
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Abstract: Let $ X$ be a $ {T_2}$ Baire space. A set $ F \subset X$ is closed and nowhere dense in $ X$ if $ F$ is the set of points of discontinuity of a function with a closed graph from $ X$ into $ {R^n}$. Although the converse does not hold in general, it does hold when $ X$ is the real line.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0334132-8
Keywords: Baire space, closed graph, closed and nowhere dense sets
Article copyright: © Copyright 1974 American Mathematical Society